Question

which solution finds the value of x in the triangle below? sec 60° = 8/x 2 = 8/x 2x = 8 x = 4

Explanation:

Step1: Recall secant definition

$\sec\theta=\frac{\text{hypotenuse}}{\text{adjacent}}$. In the right - triangle, for the $60^{\circ}$ angle, $\text{hypotenuse} = 8$ and $\text{adjacent}=x$, so $\sec60^{\circ}=\frac{8}{x}$.

Step2: Substitute secant value

We know that $\sec60^{\circ}=2$, so the equation becomes $2=\frac{8}{x}$.

Step3: Cross - multiply

Cross - multiplying gives $2x = 8$.

Step4: Solve for x

Dividing both sides of the equation $2x = 8$ by 2, we get $x = 4$.

Answer:

$x = 4$